two uniform disks are touching other at a single point. Friction at the point of
ID: 1572351 • Letter: T
Question
two uniform disks are touching other at a single point. Friction at the point of contact does not allow the wheels to slip; if one wheel rotates, both wheels rotate together. the masses and radii of the two disks are m1, m2, r1, and r,2, with m1/m2=r1/r2. suppose that a clockwise torque t is applied to the first disk. if there are no other torques on the system, what is the magnitude of the angular acceleration of the second disk? Note: the moment of inertia of a uniform disk about its center is 1/2 MR2
Explanation / Answer
The formula related to torque and angular accleration is
T = I * alpha
here I is moment of inertia
moment of inertia of first disk 1/2 m1 r1^2
moment of inertia of second disk 1/2 m2 r2^2
T_net = I* alpha
r1* F = ( 1/2 m1 r1^2+1/2 m2 r2^2) * alpha
r1 * m1 g = ( 1/2 m1 r1^2+1/2 m2 r2^2) * alpha
alpha = 2 * r1 * m1 g/m1 r1^2+ m2 r2^2
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